So short story, I just made some social medias accounts with my new name Eluut_wares and cant find if i google it.

The older name is super easy to find online, but i did organic growth over the years so i never considered marketing or SEO, so its this because it takes a while for google to get up to date? how can i make my new name easy to find?

this is important for me because my main marketing tool will be the name in the images I post online.